Question

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol μ

, e.g. mu >
1 for the mean is greater than 1, mu <
1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.)

(a) The diameter of a spindle in a small motor is supposed to be 4.4 millimeters (mm) with a standard deviation of 0.12 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 20 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 4.45 mm.
H0
:
Ha
:
(b) Harry thinks that prices in Caldwell are lower than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $21.95 with standard deviation $0.51. He takes a sample from 5 local Caldwell stores and finds the average price for this same brand of detergent is $20.08.
H0
:
Ha
:

Answer 1

For spindle diameters, the null hypothesis is that the mean diameter is 4.4 millimeters, and the alternative hypothesis is that the mean diameter is not equal to 4.4 millimeters. For local prices, the null hypothesis is that the mean price is equal to the nationwide average of $21.95, and the alternative hypothesis is that the mean price in Caldwell is lower than the nationwide average.

Step-by-step explanation:

When formulating null and alternative hypotheses for a hypothesis test, we compare a sample statistic to a population parameter to determine if there is evidence to support a certain claim. The null hypothesis (H0) states that there is no effect or no difference, and it is what we assume to be true until we have evidence to support the alternative hypothesis (Ha).

Situation (a)

For the spindle diameter situation, here are the hypotheses:

H0: mu = 4.4 (The mean diameter is 4.4 mm)

Ha: mu not = 4.4 (The mean diameter is not equal to 4.4 mm)

Situation (b)

For Harry's hypothesis about local Caldwell prices, the hypotheses would be:

H0: mu = 21.95 (The mean price is equal to the nationwide average)

Ha: mu < 21.95 (The mean price in Caldwell is lower than the nationwide average)